Dissipative quantum dynamics and optimal control using iterative time ordering: an application to superconducting qubits

Abstract

We combine a quantum dynamical propagator that explicitly accounts for quantum mechanical time ordering with optimal control theory. After analyzing its performance with a simple model, we apply it to a superconducting circuit under so-called Pythagorean control. Breakdown of the rotating-wave approximation is the main source of the very strong time-dependence in this example. While the propagator that accounts for the time ordering in an iterative fashion proves its numerical efficiency for the dynamics of the superconducting circuit, its performance when combined with optimal control turns out to be rather sensitive to the strength of the time-dependence. We discuss the kind of quantum gate operations that the superconducting circuit can implement including their performance bounds in terms of fidelity and speed.

Quantum Control of Frequency-Tunable Transmon Superconducting Qubits

“…1(b). Alternatively to standard optimal control theory [16][17][18], we achieve this limit making use of semianalytic controls, presented below, that allow us to identify and correct several sources of error when designing the drivings. These controls are divided into two families.…”

“…where c is an arbitrary constant that we take as the initial gap of the problem, c = ω(0), for convenience, and ρ ≡ ρ(t) is a free function satisfying (17),…”

“…This generic model [18,30] describes the decoherence of a damped harmonic oscillator subjected to white Gaussian noise and captures the particular setup specifications and source of errors of the transmon system through the rates γ 1 ∼ T −1 1 and γ 2 ∼ T −1 2 , inversely proportional to the characteristic relaxation and pure dephasing times T 1 and T 2 , respectively. As shown in Fig.…”

Analyzing the positivity preservation of numerical methods for the Liouville-von Neumann equation

“…The algorithm bases on Krylov subspace methods [28,29] like the approaches presented in [30,31]. A similar technique is described in [7,32,33], where the matrix exponential function is expressed using Chebychev polynomials. It should be noted that while the algorithm using the action of the matrix exponential is designed for the application in Liouville space only, the other methods may be used in both Liouville space and regular representation.…”

Special issue in honor of Eberhard K.U. Gross for his 65th birthday

“…In [112], Pronobis et al discuss a very recent approach to the study of quantum systems, namely machine learning, and how it can be used to capture intensive and extensive DFT/TDDFT molecular properties. Basilewitsch et al combine a quantum dynamical propagator that explicitly accounts for quantum mechanical time ordering with optimal control theory, and apply it to superconducting qubits [113]. In [114], a screened independent atom model is presented for the description of ion collisions from atomic and molecular clusters.…”